Should Mathematicians Care About Communicating to Broad Audiences? Theory and Practice

Panel discussion organised by the European Mathematical Society (EMS)

Should mathematicians care about communicating to broad audiences? Theory and practice

Transcription coordinated by Jean-Pierre Bourguignon, CNRS-IHÉS, Bures-sur-Yvette, France

In most countries, mathematics is not present in the media at par with other basic sciences. This is especially true regarding the communication of outstanding new results, their significance and perspectives of development of the field. The main purpose of the panel discussion, an EMS initiative, that took place at the ICM on Wednesday, August 23, between 6 and 8 p.m., was to nurture the debate on whether communicating about mathematics, as a thriving part of science, is needed, and how such a communication can be efficiently tuned to different audiences and a variety of circumstances. For that purpose, the EMS Executive Committee set up a committee consisting of Jean-Pierre Bourguignon (Centre National de la Recherche Scientifique and In- stitut des Hautes Études Scientifiques, Bures-sur-Yvette, France), Olga Gil-Medrano (Universitat de València, Spain), Ari Laptev (Kungliga Tekniska Högskolan, Stock- holm, Sweden), and Marta Sanz-Solé (Universitat de Barcelona, Barcelona, Spain) to prepare the event and select the panelists. Jean-Pierre Bourguignon was asked more specifically to prepare the event with the panelists and to moderate the discussion itself. These proceedings include a revised version of the presentations made by the panelists under their signature, and a brief outline of the discussion that took place after their presentations. A contribution that was later elaborated by a participant from the floor has been added separately from the discussion.

Philippe Tondeur (University of Illinois at Urbana-Champaign, United States of America) The question to the panelists was, as stated in the title, “Should mathematicians care about communicating to broad audiences?” My view is that of course they should, and the core of the argument is as follows: (1) Mathematics is a fantastic form of human thought, and historically the basis of rational thinking. (2) Aside from its intrinsic beauty and power, mathematics is indispensable for the progress of science and the betterment of the human condition.

(3) Mathematics is embedded in science and enables the science enterprise, even if this role is often invisible to the outsider. (4) Mathematics and science are the greatest human enterprises ever undertaken to understand the world. Mathematicians are key partners in this process. For the purpose of this discussion mathematics is used as shorthand for mathematics and statistics. Stochasticity is an essential and pervasive aspect of the phe- nomenological world. The role of mathematics in society at large Mathematics and science cannot fully progress without the understanding of their purposes and participation by the society in which this enterprise is embedded. In communicating with broad audiences, the message has to be calibrated to the specific audience addressed. This is most effective if done through examples. There is enormous public interest in the biomedical realm, thus illustrating the role of mathematics in medical progress like biomedical imaging has immediate appeal. If the mysteries of the cosmos and string theory are under discussion, the rich geometric ideas underlying these efforts can be described. Cryptography is used in telecommunication and security issues are of paramount public interest. Everyday use of search engines on the web is based on mathematical page rank algorithms. The logistics of supply chains is encountered ever more frequently in everyday life. There are vast amounts of online visual material on such topics from the mathematical sciences, and public presentations can draw on these abundant sources. This discussion also points to the critical role that mathematics plays in interdisciplinary activities. Mathematics acts as a lingua franca of interdisciplinary science. While interdisciplinary science is driven by the nature of specific science problems, it frequently operates within a contextual and quantitative framework provided by the mathematical sciences. The foreseeable future is going to be one of unprecedented pervasiveness of mathematical thought throughout the sciences. In a data driven world, mathematical concepts and algorithmic processes will be the primary naviga- tional tools. This makes mathematics increasingly important for many of the science and engineering advances to come. The opportunities for the mathematical sciences seem unprecedented. What it takes to get mathematics thriving Much of the public discussion of mathematics and science focuses on the proper level of financial support. But the vitality of the mathematics and science enterprise depends on much more than this. It is a societal activity which is part of the cultural mosaic and which flourishes especially well in an open liberal society. By this I mean a society where inquiry is respected as a fundamental principle independent of the outcome, and where all authority is understood to be provisional. The international character of the mathematical sciences makes it a model for scientific partnerships across the world. This common purpose is pursued in exemplary fashion by other disciplines like astronomy, physics, chemistry, biology, to name a few. The basic sciences are all working to develop our common patrimony. Should mathematicians care about communicating to broad audiences? 739

The educational needs for success in interdisciplinary activities are manifold: aside from mathematics, modeling, and computation, there is a need for education in the fundamentals of the basic sciences, and the development of communication skills. This requires significant improvement in our current educational paradigm for mathematical scientists. A paradoxical situation There is a paradox developing between the increased sophistication of mathematical science research and the worldwide decline of the number of students interested in pursuing mathematics at the university level. A particular threat is the insufficient number of mathematically qualified students willing to become teachers of mathematics. Mathematicians have an educational stewardship responsibility, which is primary in post-secondary mathematics education, but we also share an important responsibility in the training of teachers of mathematics. In a broad sense, mathematical scientists share in the responsibility for the state of mathematical education in the world. I am referring to education in the broadest sense, namely the preparation for lifelong learning of a large segment of the population, however that may be achieved. I would like to compare the need for mathematical skills of future generations to the current need for reading skills. It took a long time to achieve widespread reading literacy, and it will take a long time to achieve widespread mathematical literacy. Yet there is no doubt that this will be a fundamental skill in an increasingly digital world. The participation of research mathematicians in these developments is indispensable. Conclusion The gift of mathematical talent allowed us individually to enter the world of mathematics, and to enjoy this most fantastic achievement of mankind as our profession. This privilege gives rise to the responsibility of sharing these insights with our fellow human beings and especially with the next generation. My experience has been that effectiveness in these endeavors is the result of well and strongly articulated convic- tions, using all communication tools available and adapted to specific audiences.

Marcus du Sautoy (University of Oxford and an EPSRC Senior Media Fellow, United Kingdom) Maths for the masses One of the books that excited me as a child about the mysterious and romantic world of mathematics was Hardy’s “A Mathematician’s Apology”. As an adult it is a book I love and hate because it comes with a very mixed message. Anyone who wants to emulate Hardy and bring the subject alive for others lives under the spectre of the opening sentence of the book: “It is a melancholy experience for a professional mathematician to ﬁnd himself writing about mathematics. The function of a mathematician is to do something, to prove new theorems, to add to mathematics, and not to talk about what he or other mathematicians have done.” 740 Panel discussion organised by the European Mathematical Society

And this is the impression that many in the mathematical community have: anyone who talks about mathematics is a failed mathematician. So it was with a lot of trepidation that I made my own first steps to bring mathematics to the masses. A personal experience We must all as mathematicians have had the experience of trying to explain at a party what it is we do provided that discovering we are mathematicians doesn’t make the guest flee in the other direction. At one dinner in Oxford my neighbour turned out to be the Features Editor of the Times. He said that what I did sounded very sexy and would I write him an article. The next morning I found his card in my jacket pocket but realised I didn’t have the nerve to go in front of my mathematical peers saying the things I’d explained the night before. But there is an old adage in Oxford that the academics might change but the guests remain the same. So three years later I found myself sitting next to the same journalist. “You never wrote me that article.” Impressed that he’d even remembered after three years and feeling a little more confident in my position I decided to take him up on the offer. After all Hilbert had declared in his famous 1900 address to the ICM that “A mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first man whom you meet on the street.” So I decided to take up the Times and Hilbert’s challenge. I chose to write a piece about the Fields Medals which had been awarded that summer in 1994 which had got no press coverage in the UK. The piece was partly about why it hadn’t been reported. I decided to tell people what a Fields medal was (this was before Matt Damon had made them famous in the film Good Will Hunting) and what Zelmanov had done to win one. It went out in December 1994 under the banner “Why doesn’t maths have mass appeal?” A few months after that article I started a ten year research position with the Royal Society which relieved me of any teaching duties. But I couldn’t do research all the time. It would send me crazy. So I decided to dedicate some of the time that I might have been teaching to try to bring maths to the masses. I had a lot of support from the Royal Society who was trying to create better dialogue between Science and Society after a government report criticizing the separation between the two groups. Since those first beginnings I have written numerous articles about mathematics for the broadsheet newspapers, including a piece on why Beckham chose the 23 shirt to play in for Real Madrid1. Some of these articles then formed the basis for a book I subsequently wrote called The Music of the Primes about the Riemann Hypothesis. I also started doing radio work. I contacted the BBC and asked if they’d like me to cover the Seattle meeting in 1996 to celebrate the centenary of the Prime Number Theorem. They gave me a tape recorder and we did a five minute piece on the BBC’s science programme about the Riemann Hypothesis. Having found a user-friendly

1They can be found at plus.maths.org/issue26/features/sautoy/. Should mathematicians care about communicating to broad audiences? 741 mathematician, I’ve now done extensive work for BBC radio culminating in a series for the BBC called Five Shapes which I wrote and presented2. A challenge: bringing mathematics to TV screens The real breakthrough in recent years has been cracking television’s fear of doing mathematics. Simon Singh’s programme on Fermat’s Last Theorem was the last serious television outing for mathematics in England and that was over a decade ago. In the summer of 2005 I made an hour long documentary for the BBC about the Riemann Hypothesis based on my book The Music of the Primes. It went out as the centre piece of Maths Night on the BBC. Thanks to CGI effects, I realised a lifelong dream to walk through Riemann’s zeta function. Other TV work includes: – a movie about Euclid’s proof of the inﬁnity of primes using my football team who, inspired by the galácticos in Real Madrid, all play in prime numbers3; – four movies for teachers4; – and I’m currently preparing ﬁve one hour programmes that will be broadcasted on national television over Christmas. Taking a broader view Communicating mathematics to a broader audience is a rewarding but an exposing experience and you need to have a thick skin to be able to deal with criticism. Math- ematicians care about details. It is what makes for a good mathematician. But going for the grand sweep of the story is what is needed when talking to the media. Sitting in some seminars I think we still have a lot to learn about communicating between ourselves not just to a wider audience. An understanding of how to empathize with a broader audience could well help our internal communication within the mathematical community. I have had wonderful support from many colleagues for the efforts I’ve made especially in my department in Oxford. It is important to support and help those journalists and mathematicians making an effort and not to sit back and carp at an inaccurate description of the Poincaré conjecture. Why should we take the time to communicate to a broader audience? Our subject dies without new people coming into the subject. Some countries have seen student numbers in mathematics declining so much that they are closing mathematics de- partments. The next generation of mathematicians depends on the current generation telling them why the subject is so exciting. But our audience should not just be the young. It is politicians and business that hold the money and the power. They will not value our subject if we don’t show them it is important. A personal lesson One has to be proactive if you want news coverage. This year, unlike in 1994, there was extensive reporting in the UK for the Fields medals and the Perelman story. But it

2The series can be found at www.bbc.co.uk/radio4/science/fiveshapes.shtml. 3To be found at www.spiked-online.com/Sections/Science/ScienceSurvey/films.shtml. 4They can be found at www.teachers.tv/series/4289. 742 Panel discussion organised by the European Mathematical Society didn’t come from nowhere. I rang the Guardian and the BBC and other news outlets to warn them about the upcoming news story. The press office in Madrid worked tirelessly to get the fantastic international coverage that the ICM had this year. If we don’t sell them the stories, journalists are not going to come looking for them. The IMU in conjunction with national research councils might sensibly look to establish a network of mathematical ambassadors in each of its member countries who could play the same role that I tried to do this year in the British media. In the UK the need to have scientists who can communicate their subject to society has been recognised. I have a grant from my research council that goes to my department in Oxford to pay for someone else to do my teaching so that I have that time freed up to do media work. Research councils have to be proactive in encouraging people to communicate rather than expecting them to do it in their spare time, time which is already running in the negative. I believe Hardy was wrong to say that a mathematician can’t do and talk about mathematics at the same time. He would never have been melancholy about someone who is a good teacher suggesting that they must be a failure at research. Many of us combine fantastic teaching with research. So why can’t communicating with the masses and being a good researcher go together? We are seeing more examples of people breaking Hardy’s picture. Timothy Gowers, Fields Medal winner eight years ago, and Barry Mazur are two leading researchers who have made great efforts to broadcast the mathematical message more broadly. It is a quote from the Opening address of the 1952 ICM that I would prefer to be remembered rather than Hardy’s melancholy message. Oswald Veblen opened the congress by saying: “Mathematics is terribly individual. Any mathematical act, whether of creation or apprehension, takes place in the deepest recesses of the individual mind. Mathematical thoughts must nevertheless be communicated to other individuals and assimilated into the body of general knowledge. Otherwise they can hardly be said to exist.” We are all involved in telling stories of our mathematical discoveries. That is what the ICM is about. But let us be proud of our subject and share our stories beyond the confines of the ivory tower of the ICM. A recent survey in the New Scientist indicated that readers wanted more maths stories. It is the mathematicians who are best placed to tell those stories.

A. B. Sossinsky (Institute for Problems in Mechanics, Russian Academy of Sciences, and Poncelet Laboratory, Centre National de la Recherche Scientifique and Indepen- dent University of Moscow, Moscow, Russia) Promoting mathematics: why, how, who? Being Russian, I am supposed to possess this inscrutable Slavic soul, prone to seeing the dark sides of our existence. Accordingly, my talk will be more emotional and Should mathematicians care about communicating to broad audiences? 743 pessimistic than those of my Western colleagues. In it, I will try to express my concern about the problems addressed by this Round Table. For the outset, we are faced with the following sad and paradoxical fact: “mathematics, the most universal and useful of all the sciences, is the least known to the general public.” Everyone knows aboutAlbert Einstein, Wernervon Braun, and Sigmund Freud, but who has ever heard of Kurt Gödel, John von Neuman, Serge Novikov, or John Milnor? Most of us here are research mathematicians, and very proud of our profession, yet the man in the street does not even know that such a profession exists! For him mathematics, besides having been the most unpleasant subject in school, is just a specific fixed body of knowledge that some people have to learn and then apply in practice, say in engineering or accounting. In 45 years of my life as a research mathematician, I have witnessed the spectacular expansion of mathematics into practically all fields of knowledge. Besides its traditional spheres of application (physics and technology), mathematics now plays a key role in chemistry, biology, earth sciences, and even in linguistics, psychology, the social sciences, political and military strategy. During the same period, I have sadly observed – haven’t we all – the degradation of mathematical education at all levels, followed by what I call the demonization of mathematics and the deification of the computer. By the latter, I mean the common opinion that whenever you want to find out something or solve some problem, all you need to do is ask the computer – it will oblige, immediately and without any possibility of error. It is the Computer (with a capital C) that gives you the answer; the fact that a mathematician invented the algorithm used by the machine and a programmer implemented it remains unnoticed by the general public. On the contrary, it is the mathematician who is viewed by most as a soulless individual using abstruse computations to create new technologies without regard to our well being or the ecology of our planet… In Russian literature, especially in the writings of the great novelists of the end of the nineteenth century, social and ethical questions are at the forefront. Observing each serious mishap of our sorrowful history, Russian writers traditionally ask the following two sacramental questions: (1) Who is responsible? (2) What must be done? Let me try to answer these two questions in the context of our discussion. Who is responsible? To my mind, the answer is clear: we all are. We missed the great opportunity that we had, in the past two or three decades, to promote mathematics by capitalizing on its spectacular expansion. We have been overtaken and left far behind by the Bill Gates and Sergey Brin of this world. Why did this happen? One of the principal reasons is that mathematicians are usually poor communicators. 744 Panel discussion organised by the European Mathematical Society

This is related to the psychological nature of the typical mathematician: introverted and timid in his teens, he starts doing math, the most competitive and most objective of the school subjects, to assert himself; having succeeded, he develops a sense of his intellectual superiority and tends to become arrogant, at least when discussing his favorite subject. This mixture of timidity and arrogance, which I have observed in many of my colleagues (including myself, I am sorry to say), is the worst possible combination for one who wishes to communicate with others. You have surely heard both of the following allegations from your colleagues – the layman can’t possibly understand what I do! – the mathematician can do it better! You may even agree with them (I do), but what a disaster if they are in your mind at the starting point of a discussion about your profession with the nonspecialist! Another trait of mathematicians, disastrous for communication, is the ivory tower mentality, the desire to do one’s mathematics in peace and isolation from the world. A laudable viewpoint, but hardly productive for the propaganda of mathematics. What must be done? To put it succinctly, we must make mathematics visible and appealing. There are many ways of doing this, and most of them are well known. Let me simply list a few without commentary, and briefly describe one or two that may not be familiar to some of you. Visibility can be achieved via TV, art, photography (e.g. fractals), movies, exhibitions, internet sites, math-fests, popular science magazines, books, animations. As an example of the latter, let me mention the web site www.etudes.ru, which has numerous captivating and dynamic animations presenting recent mathematical results with clarity, humour, and graphical perfection. Appeal must be differentiated depending on the targeted audience. For teenagers, our future successors in the mathematical profession, there are olympiads and other individual problem-solving competitions, math circles, team competitions (such as the Kapp Abel contest for the Scandinavian countries), summer camps, “math rooms” in some schools (there is even a “math house” in Iran), so-called math battles. A few words about the latter, which are practically unknown outside of Russia, but have become extremely popular there in the last decade. This is a team contest: two teams of six are given six problems to solve (with a few hours to prepare), then, as the actual “battle” begins, they take turns in challenging each other to solve one of the problems. During each of the six rounds of the battle, a member of one of the teams is at the board explaining his team’s solution, a member of the opposite team asking questions (verifying the presented solution, i.e., trying to find and point out possible mistakes), the jury (usually consisting of two or three ordinary high school teachers, not olympiad wizards) watching the proceedings and dividing the points for each problem between the teams. The problems are ordinary high school math, Should mathematicians care about communicating to broad audiences? 745 the good math teacher and any good student (not especially interested in, or good at, olympiad problems) from an ordinary class are capable of solving them, so that math battles are for the masses, not the elite. Their appeal is due to the pleasure that the students derive from the teamwork involved, to the excitement of the battle itself (as a rule, the proceedings are very emotional), to the active participation and support of the teachers (who usually feel left out in olympiad-style competitions). The result is that many students, including those who are not thinking of a career in mathematics or engineering, learn that math can be fun, that it can be useful not only for engineers and accountants. Let me note that Russian mathematicians are traditionally good at outreaching to high school students, and a good deal of the Russian experience can be used with success in other countries. An excellent web site for information about this is www.mccme.ru (although the English version does not contain all the material from the one in Cyrillic). Reaching out to wider communities A different approach to making math appealing must be used when we are outreaching to other categories of people. Besides teenagers, I would distinguish the following three important categories: other scientists, businessmen, politicians & bureaucrats. Obviously, the approach in each case must be different, but I don’t want to go into details, because my own experience here is rather limited (and, I should add, not too successful). Other aspects of the promotion of mathematics are icons, logos, and catchy titles. It would be great if math had a photographic icon as striking as the famous Che Guevarra black and white outline photograph or as the marvelous photo of Albert Einstein absent-mindedly looking around his office with unseeing eyes, obviously engrossed in the workings of his inner mind. Or a simple but original graphic logo (as easily recognizable as the ones for Mercedes or Nike). The IMU has understood this, and recently sponsored a contest for such a graphic design symbolizing mathematics. The winning design is a version of the Borromean rings, which, frankly, I have found disappointing. I would have preferred a nice version of the Möbius band, but that has already been appropriated by Renault. The choice of terms for various branches of mathematics is also important. An excellent example is the catchy title “catastrophe theory”, which became very popular, especially in the UK, due to its promotion by Christopher Zeeman in the 1970s. In public lectures, on TV and radio, Zeeman (a great lecturer and communicator) succeeded in convincing the British public that mathematics consists of the theory describing continuously evolving events (created by Newton and his followers) and the recently created mathematics of catastrophe theory, which describes events occurring discontinuously, by leaps and jumps. Some mathematicians (especially those working in singularity theory, as the theory in question was originally called) felt annoyed by what they regarded as non-objective and demagogical exploitation of their serious work. Personally, although I can easily understand their feeling, I believe that the 746 Panel discussion organised by the European Mathematical Society campaign for publicizing catastrophe theory was useful in displaying a positive image of mathematics. Of course one shouldn’t go too far in publicizing exaggerated claims about the achievements of mathematics, but certainly a lot of oversimplification and a little exaggeration are needed for success. Besides catastrophe theory, there are several other branches of mathematics with catchy titles: tropical mathematics, quantum computing, open-key cryptography, chaos. These terms will easily catch the attention of the general public if they are used systematically in talking about mathematics. The influence of a catchy title should not be underestimated, sometimes a clever choice of title will lead to successful promotion of the subject, even when intrinsically it is not really worthwhile (which is not the case of the branches of mathematics with the catchy titles listed above – they are all serious, interesting and useful mathematics). A striking example is so-called “fuzzy mathematics”: after a promising start in the well-known paper by Bellman and Zadeh, the topic with that title developed into an industry producing numerous publications and PhDs, which were, in my opinion, devoid of any serious mathematical content. I am sure that if it had been entitled, say, “approximative mathematics” no one would have paid much attention to it. Yet another way to attract ordinary people to mathematics is by showing them mathematical machines, i.e., various mechanisms demonstrating curious mathematical effects. An extremely successful example is the prime time TV programme on one of the national channels in Japan, in which mathematical ideas are described and made visible by demonstrating the functioning of various mechanisms. The name of the creator of this program, Akiyama, is a household word in Japan, as popular as, say, Larry King in the US. Another example of physical models of mathematical ideas is Chris Zeeman’s well-known “catastrophe machine”. But all of the above will remain wishful thinking, unless we decide who is going to implement it. Who must do it? Again, the answer here is obvious: all of us should, each of us doing whatever is suited to his or her position and aptitudes. The rank and file mathematician, first of all, should not be afraid to talk about mathematics in an attractive, perhaps humorous or emotional way, to friends and relations: his or her spouse, tennis or golf partners, neighbors. The inspiration for such short conversations can be provided by Hilbert’s quotation (whose exact phrasing was given in Marc du Sautoy’s talk) asserting that any worthwhile mathematics can be explained to the man in the street. The worst possible thing that you can do is to give definitions of the main concepts involved and then state the result(s) of your own work: your interlocutor will be disoriented and bored. Before trying to explain what your work is about, you might begin by making clear that mathematics is a living, exciting, competitive activity – without declaring this directly, but by talking about your rivals and/or collaborators in other countries, about how long your field of study or the problem you are attacking Should mathematicians care about communicating to broad audiences? 747 has been occupying mathematicians, about the excitement you feel when the result you want is achieved or escapes you. You might then explain that mathematics differs from all the other sciences is that it does not necessarily have a specific object of study from real life: the same differential equation can describe completely different processes in nature, the same surface can portray all the positions of a mechanical system as well as elementary particles in quantum physics, the same formula be applicable to knots and to the phase transfer that occurs when water is transformed into ice. (You shouldn’t worry about the fact that the person you are talking to does not know the formal definition of “differential equation”, “knot”, “surface”, “phase transfer” – after all, everybody talks about television sets and mobile phones without having the least ideas about how these devices work.) What makes mathematics so effective, you might add, is that one never knows in advance what it may be applied to. You might continue by giving examples of mathematical situations when it turned out that a solution of some problem eventually had spectacular applications to real life situations that the researcher certainly did not have in mind when working on the problem. When I am engaged in such informal conversations with a friend or acquaintance, I like to give concrete examples from my own research experience. Thus, in answering a question like: – “What do you guys in mathematics actually do?”, I might say something like this: –“Of course I do some teaching, but what I am really interested in, what really excites me, is trying to discover new facts in mathematics.” –“There are really new facts to discover in mathematics? Like what?” This leaves me with many possibilities of continuing the conversation, usually by referring to some of my own work or something related to it. Thus I might say: – “Well, I’m supposed to be an expert in the theory of knots and braids. Let me tell you about braids. A braid is a geometric object that looks like several strings hanging down from a horizontal stick and interlacing with each other. The way they are studied is by means of algebra: we replace the overcrossings by special symbols and develop a calculus with these symbols that allows to answer all the complicated geometric questions about braids by means of simple calculations that I can perform by hand or let my stupid computer work out.” The reaction to that is usually skeptical or negative: – “But what’s the use of doing that?” This gives me the chance to come to the punch line of the story. I explain how my rival and friend, the French mathematician Patrick Dehornoy, together with one of his graduate students, used the calculus of braids to construct a new “one-way function”, then explain how one-way functions are used in electronic banking, and conclude that someday my interlocutor’s credit card will be protected from electronic theft by…braids. 748 Panel discussion organised by the European Mathematical Society

I have several ready-to-use stories like that up my sleeve (prime knot decomposi- tion, homology of tolerance spaces and numerical solutions, soap films and random walks). Let me add that I have a new one in preparation: I have done some work related to the Poincaré conjecture, and now that it has been solved by Grigory Perelman, I have a good pretext of telling anyone who wants to listen about the dramatic story of Hamilton and Perelman, the later’s refusal of the Fields medal and his apparent disinterest in the Clay Institute’s million dollars. In the process of telling it, I will not be afraid to say that the main idea of the proof is the seemingly completely crazy idea to apply something resembling the heat equation to solve a purely topological problem. I will not bore this audience by retelling these stories here, but I would like to appeal to all mathematicians to have such stories (preferably related to their work) at their disposal, enabling them to give well rehearsed impromptu five-ten minute talks for the benefit of non-mathematical acquaintances and friends. Of course more formal popular presentations (e.g. public lectures) are also very useful, provided they are well done. But then not everybody can be an Ian Stewart or a Petar Kenderov, and very few people can give such deep and visually striking talks as the one of Étienne Ghys at this Congress. (If it were up to me, I would make a video of that talk and distribute it among all the leading universities of the world.) The math administrator at a university or college, e.g. the chairperson of the math department, besides all that he or she can do as a mathematician, should feel that it is his or her direct duty to attract the best students of the institution to major in math. This can be done by outlining the advantages of our profession (no 9-to-5 drudgery, lots of travel, sabbaticals, long vacations), the career opportunities outside of research (you can tell the students that banks and other financial institutions prefer to hire, at very high starting salaries, PhDs in math or mathematical physics from Harvard, rather than people with an MBA or a PhD in computer science from the same university, or explain that the most successful people in the computer software industry are usually math majors, not students who majored in computer science). Of course another important function of the math administrator is to attract money to math research. This can be done by outreaching to those who have the money, via the mass media and in other ways, stressing how useful mathematics can be. The math research institutes (such as IAS, IHÉS, MSRI) must address a different class of people in their promotion of mathematics: graduate students and post docs should be the first to be targeted, and of course the people and organizations that have money and might agree to part with it. The research institutes can also sponsor other activities. As a positive example, let me mention that the director of MSRI, David Eisenbud, is organizing a conference in Moscow this fall in order to familiarize American mathematicians with the Russian experience in running math circles. I also firmly believe that, in order to make the promotion of mathematics efficient, not withstanding that “the mathematician will do it better”, the research institutes should hire experts in public relations to coordinate and organize promotional activities. Should mathematicians care about communicating to broad audiences? 749

The EMS, the AMS, and the IMU, I ﬁrmly believe, should do much more to coordinate the promotion of mathematics at all levels in Europe, America, and worldwide. First of all, they should motivate and assist their members to advertise their profession and their science. This can be done, in particular, by distributing electronic or hard copy booklets or brochures explaining to individual mathematicians what they can do and how to go about it, and also by supporting and organizing various promotional activities of the kind I described previously. I am convinced, and this is a crucial point, that math must be promoted in a professional way, a qualiﬁed public relations professional hired by the corresponding Society should be responsible for these activities. Conclusion Starting from a pessimistic assessment of the situation, I have progressively drifted to advertising mathematics. When you advertise, you must always end on an optimistic note. So let me say, in conclusion, that if we all pitch in, mathematics will reacquire the prestige and renown that it deserves in our society. And since we are in Spain, let me end with the following slogan: Adelante, matemáticos!

François Tisseyre5 (Atelier ÉcoutezVoir, Paris, France) Producing media with mathematicians I will be speaking in the name of Atelier ÉcoutezVoir, a non-for-proﬁt organization initiated 30 years ago in Paris. This studio is mainly dedicated to communication of art and science through audiovisual production. Concerning mathematics, we have been working in the ﬁelds of Engineering Sci- ence, Applied and Fundamental Mathematics. During the past 25 years, we have had the pleasure to work with a few mathematicians who wished to communicate with various audiences, ranging from children to professional mathematicians. Thus we have produced a number of videos, visual presentations, exhibitions, and taken part in various events like festivals, congresses or meetings. I would like to concentrate on video production, which is what we do most. In practice, we start working when the mathematician has already answered the global question we are discussing today. For social, or moral, or generational reasons, his or her answer is “Yes, of course”. Then quite a few questions arise. Here are some of the ones we have had to cope with.

5I want to dedicate this text to Adrien Douady who recently and tragically passed away. In the last twenty years, his fame as mathematician extended to one of a patient and innovative communicator. His contributions to the popularisation of mathematics have taken several forms: as author and scientiﬁc director of audiovisual projects (e.g. La dynamique du Lapin), of the exhibit “ A fractal world” that he accompanied in several countries, of many colorful conferences, he reached out to broader and broader types of public, further and further away from his fellow mathematicians. In the decorum of established institutions as well as in a café in rue Mouffetard, in Paris, Adrien always showed an exceptional openess to tirelessly explain the most abstract notions to anybody who was willing to listen to him, most of the time from a surprising angle leading to new fruitful insights. A DVD with his many contributions is under preparation. 750 Panel discussion organised by the European Mathematical Society

Motivation The mathematical community does not seem to have a unitary attitude in front of transmission and share of knowledge. Many mathematicians just dream to transmit the great pleasure they feel as they do maths. Of course, one has to practice maths before he/she knows it can be a pleasure. Some think that the general population suffers from “innumeracy” and has to be cured. Others feel that it is their duty to transmit what they get payed for, generally through public funding. Quite a number do not want to be disturbed with such questions, because they want to keep concentrated on their work and talk with colleagues only. And many others… Maths and the media (France) Let us first notice that practically no maths appear on French TV, or so little, and it would certainly be helpful to try and understand why. However, various approaches are available, like: documentaries on the community, presentation and illustration of nice classical problems, introducing new concepts or disciplines, history of ideas, recording exceptional lectures, games, and so on. Fortunately today, television is not the unique horizon for audiovisual diffusion. Producing DVD’s or webcasting have become usual practice with results of increasingly good quality. So that there are effective supports for audiovisual publishing. Authors and producers are welcome, including young ones. A vital need for dialogue How can there be a fruitful dialogue between audiovisual professionals and mathematicians who intend to publish something together? When we film makers speak of video or film, we have narration in mind. Im- ages and sounds come continuously and form sequences, by construction. When we make films, we are always telling a kind of story, whatever abstract it may be. But mathematicians do not read maths like a novel, in a continuous way: they will read a paragraph, then stay half an hour studying another one, reading and reading again, then study a formula, or make computations, and so on. If we decide to work together and produce a video, we will have to define what can be presented continuously, because the audiovisual language allows that only. Another point is that we do not speak the same language. And what’s more, we do not have the same appreciation of what we have to learn in order to cooperate with meaningful results. As non-mathematicians, we producers obviously have to learn maths for every single production we undertake with mathematicians. There’s no doubt about that for each of us. And it’s very exciting. On the other hand, mathematicians do not call themselves non-producers or non-directors. Just because, like many people, they have the feeling that it is very easy to understand how films are made: writing a script, shooting with cameras, editing, and that’s all. I want to plea for a simple idea: if we want to achieve fertile results, we have to constantly make steps towards one another. A good film is found somewhere between our respective fields. So it is vital that we all make efforts to understand each other’s approach. Should mathematicians care about communicating to broad audiences? 751

Sense and meaning But the main problem may not be good will, but rather a matter of sense and meaning. The mathematician wishes to convey something that is meaningful for him or her and colleagues: an article, formulas, a conjecture, that are consistent. Our job is to help this make sense for the audience. This could seem to be a theoretical discussion. In our case, it is what takes place in practice every time we make films with specialists of any domain, especially maths. Let me give an example: ten years ago, Jean-Pierre Bourguignon proposed us to make a film about a memoir that Lagrange wrote in 1808. This appeared to be a revolutionary one in a certain way, as it opened completely new paths to study the movement of planets and many other abstract problems. During three months, Jean- Pierre tried and explain that to us. But it sounded absolutely abstract and meaningless, like an unfamiliar music. We used to speak of this with late Romain Weingarten, a French poet and writer; he was very excited too, and begged for more explanations. One day, I asked Jean-Pierre to tell us more about the three-body problem, then about Newton, and Kepler. Then we started meeting astronomers and specialists of history of science, but also space engineers, and this is how we finally found the red thread of our film: a poet is dreaming at night at his window, and he sees an artificial satellite in the sky. He asks his friend, a mathematician, to help him understand how the man succeeded in putting man-made objects among celestial ones. When we have had that scenario, it became very exciting to work with an increasing group of contributors to whom we asked to just play their own role: Jean- Pierre Bourguignon as a helpful mathematician, Jean Brette, as a marvellous maths popularizer, Bruno Morando as an astronomer, Huguette Connessa as an engineer and among them Romain Weingarten, a poet who kept dreaming aloud. The film is called The New Shepherd’s Lamp6, and we all remind this period with great emotion. There had been a deep transformation, not of the initial subject, but of its approach, and this meant something both to mathematicians and non-mathematicians. Investing in video math production How far, and how much are both sides ready to invest of time and energy? Who else is needed? For a mathematician, taking part in a video production actually requires as much time as publishing an article, or even a book. But it takes more, as much patience and pedagogy are still needed to make us at least get a flavour of the topic we are going to deal with. He or she will have to answer 10, 20 times basic or naive questions, till the music becomes familiar. Then we have to get enough practice to let our imagination go. For us, this may be quite a long and hard way to get into the subject. Here is an example again: in 1992, Adrien Douady wished to produce a series of videos to help students understand basic Holomorphic Dynamics. The first module was entitled The Dynamics of the Rabbit7; it is the study of a Julia Set. It took us nearly

6The French version of the video is available from the CNRS Images/Vidéothèque and the English one in the Videomath series edited and distributed by Springer Verlag. 752 Panel discussion organised by the European Mathematical Society

five years to produce it, and here is why and how. First, as a non mathematician, I had to learn about complex numbers, iteration, etc., and get familiarized with strange pictures (fractals). It took me about a year and a half to know enough to be able to build and discuss a pertinent script. During that period, there has been quite a lot of consulting with other mathematicians, students and teachers. Then we decided to start producing pictures, in order to show the various structures and phenomena that appear in the study. We needed to produce many, and especially animated sequences. So we had to find someone capable of producing thousands and thousands of very accurate pictures (there are 25 pics per second). Dan Sørensen was the man with this singular profile: a mathematician, and an engineer capable of developing adapted software. Dan had to take into account both the needs of the scientist and those of the film director. Then we had to find the way to transfer the computer images to video, which was not common at that time. So we had to develop specific and efficient techniques for that. We calculated more than 150,000 pictures and finally kept something like 25,000 for about 20 minutes of mute video. Adrien Douady then commented these sequences: we proposed the form of spontaneous commentary, obtained thanks to interview and accurate sound editing. After mixing, the final result is a 25 minutes video, with English and Spanish adaptations obtained thanks to mathematicians Shaun Bullett and Nuria Fagella. Finally, to give a perspective, for this project, starting with two persons, we finished with a dozen, acting successively or simultaneously. About the audience As we started the Rabbit project, we had in mind a specific audience consisting of ad- vanced students and mathematicians from other fields. But during all the production process, and especially during conception, many objectives had to be re-defined, in particular due to some repeated difficulties we met. So that there has been quite a lot of interactions between us along time. This may be seen as a difficulty. In fact it is an opportunity to make films that make sense for each of us. As we produced sequences, we used to present them to different people, and get interesting and sometimes surprising feedback. We learnt how much such images speak by themselves and give more than a flavour of the subject. This is how the audience became to get broader. Finally, the Rabbit video is presented to rather large audiences, depending on whether it is projected alone, or supported by previous presentation then exploited through discussion. Actually, the various videos we have produced are intended to these rather large audiences with little focus, as we do not work under the frame of official educational programmes. Roughly, what we now call “broad audience” includes adult people who are fond of science culture, students of various fields, even pupils of secondary school scientific sections. These persons like to understand processes and methodologies more than technical results. They read magazines, watch some rare TV programmes, and love to visit science museums.

7This video has been edited by Atelier ÉcoutezVoir, Paris, France (1996) and also reproduced in Video and Multimedia at 3ecm (S. Zarzuela, S. Xambó, Editors), Springer VideoMATH Series, Springer Verlag (2000). Should mathematicians care about communicating to broad audiences? 753

Conclusion? Among the various dimensions we explored in maths popularisation, video is the most difficult and exciting we have experienced. A common idea is that video can be a useful medium to convey mathematical concepts. This is true, as animated images and fine sound/image accordance can be efficient. But we have to keep in mind what the audience’s social habits really are. People zap. And we have to be humble regarding effective results. We are not going to have millions of people love maths thanks to videos, but video can bring a very nice taste of maths, and this might be quite a helpful way of contributing to its popularisation.

Björn Engquist (Royal Institute of Technology, Stockholm, Sweden, and University of Texas at Austin, United States of America) Audiences to be addressed Several audiences need to be addressed by mathematicians: the general public, the media, different administrations (government, universities, schools), potential students who are, no matter how one takes it, the mathematicians of the future. The main difficulty is deliver different but coherent messages to these manifold audiences. The content of the messages to be passed on The messages have to be articulated around two complementary themes: the general culture of mathematics and its applications, while keeping always in mind which message you are talking about and to whom you are delivering it. Along the culture line, one has to give due value to the long history of mathematics and the outstanding personalities that marked it. It also has to encompass the role of mathematics in education, through its role in abstract thinking but should not avoid talking about its recreational side. Via its applications, mathematics is often viewed as the third pillar of science with a major impact in everyday life, technology, and education. Mathematics is the language of quantative science even for experiments. Its impact in so many different sectors of society has grown so large that illustrative examples are plentiful: from weather prediction to signal processing, medical images, and industrial product development. One should not forget that Google is fundamentally a mathematical product. Mathematicians should learn from biologists, physicists,… A key issue is a proper understanding of the interplay between pure and applied research. The discourse that most scientists put forward is that in order to solve problems that society wants to be solved basic research is indispensable. Too often mathematicians tend to be more abrupt, and state their intention of doing basic research that may, some day, be relevant to solve some problems. The science approach is actually more effective and still does not limit freedom of basic research. From that point of view, mathematicians should not be afraid of using applications as motivation for curiosity driven basic research. Not being shy does not mean that one is allowed to overstate because mathematics is almost always 754 Panel discussion organised by the European Mathematical Society not solving the real problem alone but mathematicians are important, if not essential, partners in the solution. The universality of mathematics The strength of mathematics is its universality. In one of its facets or another, it is needed in almost all aspects of modern life. One should always have examples ready and updated. It should also not be overlooked that core mathematics also needs to be developed as foundation for all of mathematics. The case should also be made that mathematics is as fast in the relation between basic research and applications as other sciences. It will not be surprising if, for example, any practical results from the Large Hadron Collider will take longer time than it took from theorems in harmonic analysis, via wavelets, to image compression for the Internet. Jean-Pierre Bourguignon (Centre National de la Recherche Scientifique/Institut des Hautes Études Scientifiques, Bures-sur-Yvette, France) A brief summary of the discussion The discussion triggered by the five presentations was quite lively. Some colleagues wanted to share their experiences, some others to warn against possible abuses, and the possible loss of meaning about the true nature of mathematics. The need to be very much aware of the audience when making a presentation over mathematics was stressed by several people. A lack of awareness in this direction can often lead to opposite effects than the ones hoped for. This fact is again discussed in the point of view that one of the colleagues who took part in the discussion from the floor wrote up (see an excerpt from the document received by the Panel after the Congress at the end of these proceedings). The issue that gave rise to the most controversial exchanges is the risk of “overselling” mathematics, and what goes with it, namely the loss of control by scientists of the products of science. What is at stakes is of course the moral value that some colleagues place above all in the practice of mathematics, and more generally of science. For some of them, this generates an extreme uneasiness when making the case for mathematics at all price, as regards the tendency of hiding inappropriate uses of mathematics made by the society at large. According to them, the risk of losing critical sense vis-à-vis recent developments of the discipline is so high that it prevents them from participating in actions addressing large audiences about mathematics. From this point of view, the fact that the title of the Panel discussion ended with a question mark was certainly welcome. It must be acknowledged that a marked sensitivity to moral issues up to the point of creating an explicit reluctance in addressing the general public about mathematics was not represented among panel members. Such an attitude is of course related to the fact that mathematicians necessarily wear several hats when acting in society: teachers, researchers, and in a broader sense intellectual and moral references, and finally, for some of them, politically active citizens. It was stressed how difficult it is to draw a line between these different Should mathematicians care about communicating to broad audiences? 755 responsibilities, and how serious the consequences of this situation can be on the credibility of the overall mathematical enterprise. The final issue being: who controls what? Very rarely, are mathematicians running the complete show. In issues like arms production (and the “modern” battlefield does involve dealing with a lot of data, many of which of a mathematical nature or subject to a mathematical treatment) recent developments of mathematics or demands made to mathematicians can hardly be considered neutral. The key question is then: how can one keep enough distance to be sure of what is at stakes and not let the technical discussion hide some more fundamental issues? Actually, it was argued that the move towards an information society increases the mathematicians’ responsibilities. It should force them to make sure that the values they believe in are not betrayed in the way the practice of their discipline evolves. They should also make sure that such issues are not well kept secrets when talking about mathematics to various kinds of audiences. This way of approaching the question under debate made the exchange very valu- able and gave a very welcome depth to it. It also gives a reason to revisit it and to consider it with the appropriate focus: indeed, if approached at a too general or too technical level, the debate can miss some essential points.

An excerpt from the document submitted by Jacqui Ramagge (School of Mathe- matical and Physical Sciences, The University of Newcastle, Australia) I have been involved in popularizing mathematics8 at a small and local level for about 10 years. This has included interactions with the press and regular appearances on local radio as well as workshops for children of all ages, teachers (both primary and secondary) and parents. Communicating and promoting mathematics To claim that we have nothing to do is to ignore the changes that have taken place in society over the last 30 years and is selfish in the extreme. Students have a greater choice of studies than they had in the past and some areas of study are being marketed forcefully and effectively. Doing nothing is no longer an option unless we are willing to see the demise of mathematics as a discipline and the concomitant effects on other disciplines which are highly dependent on mathematical innovation. I argue that we need to raise the profile of mathematics significantly. We need to do this for two reasons, one is altruistic and the other pragmatic. The altruistic reason is that we are already at the stage where demand for qualified mathematicians and statisticians outstrips supply. The pragmatic reason is that many universities are now working as competitive environments and mathematics will lose out in terms of funding and influence to disciplines whose profile is higher. Identifying those who should be involved in the raising of the mathematical profile partly depends on the context. For example, not all of us enjoy talking to the media and

8When referring to mathematics and mathematicians, all statements are equally applicable to statistics and statisticians. 756 Panel discussion organised by the European Mathematical Society some of us might do more harm than good in that context. However, as a community, we should recognise the need for such activities and support and encourage those who do them. Some people have a talent for stripping ideas down to their very core so that the heart of the concept is exposed and can explain it in a way that makes sense to almost anyone. Those of us less talented in this area we can still improve our performance with sufﬁcient practice. While it is essential to curtail technicalities when addressing a broad audience we must not mislead the audience. This leads us neatly to the next topic. Selling and overselling mathematics Some people argue that outreach activities necessarily involve misleading the public by exaggerating the impact of mathematics. Luckily, there are enough amazing examples of the impact and applications of mathematics that we don’t need to make any up. One mistake in this context is to confuse selling with providing information. Stu- dents are increasingly concerned about their future and ask questions such as “I don’t want to be a teacher so why should I study mathematics?” We need not be evangelical, but we must give students an accurate impression of what mathematicians do. It is the responsibility of all enterprises that use mathematics and employ mathematicians to inform the population about the usefulness of mathematics. This group of enterprises is diverse and to achieve maximum impact they require coordination. Mathematicians are the obvious choice to facilitate this endeavour, and we should be proactive in this regard. This could include asking relevant organisations for support to run mathematical outreach activities. Mathematical games and competition(s) One well-established mechanism for piquing the interest of young people is to run mathematics competitions of various sizes and levels of formality. However, competitions tend to be favoured by the competitive. This may be one factor in the dis- proportionately low number of women amongst mathematics olympians for example. We could use hybrid approaches such as competitions for groups of students. One problem is that the overwhelming number of current mathematicians have been attracted to mathematics by the inherent beauty of the subject and/or competitive selection processes. This makes us a surprisingly homogeneous group given that we are spread all over the globe. It is notoriously hard to see the world through the eyes of those whose motivations are completely different from our own, but that is exactly what we have to do if we want to increase diversity in mathematics. In conclusion, if we are not seen to be passionate about mathematics, then we can hardly expect others to be passionate on our behalf.